I'm not an expert, but I think if you doubled the network for an hour blocks would be created on average every 5 minutes instead of ten and you would have a 50% chance at receiving the bitcoins generated in those blocks... so you would end up with 300 bitcoins. They would be real. You would be helping to power the network and that would be your payment.You wouldn't be able to steal anyones bitcoin or generate false ones. You could try but no matter how fast you pump out blocks no one would accept one with invalid transactions.Check this wiki page:https://en.bitcoin.it/wiki/Weaknesses#Attacker_has_a_lot_of_computing_power

It just seems weird that the total valuation of the currency (20,738,252 USD) is worth ~10x more than the price it might cost to potentially ruin it...?

You don't get everything. In fact you get almost nothing. You can rewrite recent blocks which just means that you can unpay coins you already had control of. Or you could refuse to put transactions in blocks or to build off of anyone who does effectively a DOS. But you don't get $20M by any means.

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You don't get everything. In fact you get almost nothing. You can rewrite recent blocks which just means that you can unpay coins you already had control of. Or you could refuse to put transactions in blocks or to build off of anyone who does effectively a DOS. But you don't get $20M by any means.

How about if someone with a lot of bitcoins rented a machine like that out for a short period?You could then cash in on the bitcoins several times over?

You don't get everything. In fact you get almost nothing. You can rewrite recent blocks which just means that you can unpay coins you already had control of. Or you could refuse to put transactions in blocks or to build off of anyone who does effectively a DOS. But you don't get $20M by any means.

How about if someone with a lot of bitcoins rented a machine like that out for a short period?You could then cash in on the bitcoins several times over?

What would/could happen to bitcoins after such an attack?

It depends on how much of what sort of things are being offered and on what terms. You probably shouldn't give things to strangers that are a substantial fraction of the cost of controlling the network. If someone was holding a lot of coins and did a big attack it would probably shake faith in the network and reduce the value of his coins. And he probably can't easily spend them all more than once and pull them back since word will get around fast and the most vulnerable will shutdown or reduce payouts (like ATMs and similar instant stuff).

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You don't get everything. In fact you get almost nothing. You can rewrite recent blocks which just means that you can unpay coins you already had control of. Or you could refuse to put transactions in blocks or to build off of anyone who does effectively a DOS. But you don't get $20M by any means.

How about if someone with a lot of bitcoins rented a machine like that out for a short period?You could then cash in on the bitcoins several times over?

What would/could happen to bitcoins after such an attack?

You need to distinguish honest mining from hostile mining. Honest mining is when you always build on the longest block chain. Hostile mining is when you reject blocks for nefarious reasons.

If someone rents some hardware and mines honestly, that's great, he strengthened the network and is rewarded for it. Note that when the mining reward will consist only of transaction fees, speeding up block generation will cause each one to be worth less.

If someone used the computing power to reject blocks, there's little he could do to profit from it. He can damage the network, but not catastrophically.

Does this mean a system a bit over 1.5 million dollars could take over the network and make a load of false bitcoins?

No, it does not mean that. The most profitable attack that anyone could perform on the bitcoin network if they controlled more hashing power than the entire remainder of the network would be to reclaim coins that they recently owned and spent. They could not take coins that they never owned, not even from the most recent block. Nor could they make bitcoins beyond the parameters of the system, legitimately or not.

And this attack, as difficult as it is, only lets the attacker respend his most recently spent coins because it allows an attacker to rewrite the most recent block. However, the difficulty for the attacker goes up dramaticly the farther back in the blockchain the transactions that he wishes to overwrite might reside. Otherwise the honest network will continue to outpace his total-proof-of-work, based upon how far back he must go to get at said transactions.

"The powers of financial capitalism had another far-reaching aim, nothing less than to create a world system of financial control in private hands able to dominate the political system of each country and the economy of the world as a whole. This system was to be controlled in a feudalist fashion by the central banks of the world acting in concert, by secret agreements arrived at in frequent meetings and conferences. The apex of the systems was to be the Bank for International Settlements in Basel, Switzerland, a private bank owned and controlled by the world's central banks which were themselves private corporations. Each central bank...sought to dominate its government by its ability to control Treasury loans, to manipulate foreign exchanges, to influence the level of economic activity in the country, and to influence cooperative politicians by subsequent economic rewards in the business world."